Decoding GPS satellite data at low signal to noise levels by computing total probability of current data bit at current time epoch

ABSTRACT

A method of decoding a GPS carrier signal comprising: (A) receiving a phase modulated GPS signal by using a GPS antenna; (B) extracting a GPS data from the received phase modulated GPS signal; and (C) computing a total probability of a current GPS data bit being “one” or “zero” at a GPS time epoch by using a decoding algorithm.

This is the continuation for the patent application Ser. No. 10/647,035,filed on Aug. 21, 2003, now U.S. Pat. No. 7,260,160 and entitled “METHODAND APPARATUS FOR DECODING GPS SATELLITE DATA AT LOW SIGNAL TO NOISELEVELS”.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to the field of decoding a GPS satellitedata, and more specifically, to the field of decoding a GPS satellitedata having a low signal-to-noise ratio (SNR).

2. Discussion of the Prior Art

The data stream transmitted by GPS satellites is described in detail in“Global Positioning System: Theory and Applications”, Volume 1, pages121-176, third printing, 1996. The GPS 50 bits/s (Baud) data streamincludes an important information used by a GPS receiver to perform asatisfactory navigation, to realize a valuable time transfer function,to obtain a geodetic surveying, and/or to perform a set of satisfactoryvelocity measurements. These navigation data are uploaded to eachsatellite by the GPS Control Segment (CS) for later broadcast to theuser.

More specifically, the 50 Baud GPS data stream includes (a) Ephemerisinformation including a detailed information about a particularsatellite's orbit position and clock offset, (b) Almanac informationincluding a less accurate information about all satellite orbits andclock offsets, and (c) a satellite health information, that is whetherany particular satellite should be used by a GPS receiver to facilitateposition calculation. The capability to receive all relevant GPS datafrom the combination of information obtained from the 50 Baud datastream is one of the aspects that are critical to the receiver'soperation in being able to compute position, time and velocity.

In the prior art, in low SNRs applications (for example, in indoorapplications) a typical GPS receiver fails to decode 50 Baud data. As aresult, in the prior art, the satellites emanating a low SNR data couldnot be used in a navigation solution.

What is needed is to improve a GPS receiver capability to decode a GPSdata stream having low SNR, thus enabling GPS receivers to use a low SNRGPS satellite in a navigation solution.

SUMMARY OF THE INVENTION

To address the shortcomings of the available art, the present inventionprovides a novel method of decoding a signal having low SNR.

In one embodiment, the method of the present invention for decoding aphase modulated carrier signal comprises: (A) receiving a phasemodulated carrier signal; (B) performing a frequency loop lock (FLL)tracking of the received phase modulated signal having a carrierfrequency; (C) locking on to the carrier frequency of the received phasemodulated signal by using the FLL; (D) computing inphase and quadraturecorrelation data corresponding to the phase modulated carrier signal ata plurality of time epochs; (E) computing a first partial probability ofa current data bit at a current time epoch by using the computed in thestep (D) inphase and quadrature correlation data corresponding to atleast two consecutive time epochs, each consecutive time epoch precedingthe current time epoch; (F) repeating the step (E) for a plurality oftime epochs preceding the current time epoch to obtain a plurality ofpartial probabilities of the current data bit; (G) computing the totalprobability of the current data bit by using the computed in the step(F) plurality of partial probabilities of the current data bit; and (H)outputting the current data bit as being “one” or “zero” at the timeepoch based on the computed in the step (G) total probability.

In one embodiment, the method of the present invention of decoding aphase modulated carrier signal comprises: (A) receiving the phasemodulated carrier signal; (B) performing a frequency loop lock (FLL)tracking of the received phase modulated signal having a carrierfrequency; (C) locking on to the carrier frequency of the received phasemodulated signal by using the FLL; (D) computing a total probability ofa current data bit being “one” or “zero” at a time epoch by computing aplurality of probabilities of phase transitions at a plurality of timeepochs, wherein the probability of a phase transition at a time epochcomprises a probability of a phase transition between the current phaseof the received phase modulated signal and the phase corresponding to apreviously computed data bit; (E) outputting the current data bit asbeing “one” or “zero” at the time epoch based on the computed in thestep (D) total probability; and (F) multiplying the current data bit byan absolute data polarity.

In one embodiment, the method of the present invention of decoding a GPScarrier signal comprises: (A) receiving a phase modulated GPS signal byusing a GPS antenna; (B) performing a frequency loop lock (FLL) trackingof a received phase modulated GPS signal having a carrier frequency byusing a GPS digital tracker; (C) locking on to the GPS carrier frequencyof the received phase modulated GPS signal by using a tracking andnavigation block; (D) extracting a GPS data from the received phasemodulated GPS signal; (E) computing inphase and quadrature GPScorrelation data corresponding to the GPS phase modulated carrier signalat a plurality of GPS time epochs; (F) computing a first partialprobability of a current GPS data bit at a current GPS time epoch byusing the computed in the step (E) inphase and quadrature GPScorrelation data corresponding to at least two consecutive GPS timeepochs, each consecutive GPS time epoch preceding the current GPS timeepoch; (G) repeating the step (F) for a plurality of GPS time epochspreceding the current GPS time epoch to obtain a plurality of partialprobabilities of the current GPS data bit; and (H) computing the totalprobability of the current GPS data bit by using the computed in thestep (G) plurality of partial probabilities of the current GPS data bit.

In one embodiment, the method of the present invention of decoding a GPScarrier signal comprises: (A) receiving a phase modulated GPS signal byusing a GPS antenna; (B) performing a frequency loop lock (FLL) trackingof a received phase modulated GPS signal having a carrier frequency byusing a GPS digital tracker; (C) locking on to the GPS carrier frequencyof the received phase modulated GPS signal by using a tracking andnavigation block; (D) extracting a GPS data from the received phasemodulated GPS signal; (E) computing a total probability of a current GPSdata bit being “one” or “zero” at a GPS time epoch by computing aplurality of probabilities of phase transitions at a plurality of GPStime epochs, wherein the probability of a phase transition at one GPStime epoch comprises a probability of a phase transition between thecurrent phase of the received GPS phase modulated signal and a phasecorresponding to a previously computed data bit; (F) outputting thecurrent GPS data bit as being “one” or “zero” at the GPS time epochbased on the computed in the step (E) total probability; and (G)multiplying the current GPS data bit by an absolute GPS data polarity.

In one embodiment, the method of the present invention of decoding acarrier signal comprises: (A) receiving a phase modulated signal byusing an antenna; (B) performing a frequency loop lock (FLL) tracking ofa received phase modulated signal having a carrier frequency by using adigital tracker; (C) locking on to the carrier frequency of the receivedphase modulated signal by using a tracking and navigation block; (D)extracting a data from the received phase modulated signal; (E)computing inphase and quadrature correlation data corresponding to thephase modulated carrier signal at a plurality of time epochs; (F)computing a first partial probability of a current data bit at a currenttime epoch by using the computed in the step (E) inphase and quadraturecorrelation data corresponding to at least two consecutive time epochs,each consecutive time epoch preceding the current time epoch; (G)repeating the step (F) for a plurality of time epochs preceding thecurrent time epoch to obtain a plurality of partial probabilities of thecurrent data bit; and (H) computing the total probability of the currentdata bit by using the computed in the step (G) plurality of partialprobabilities of the current data bit.

In one embodiment, the method of the present invention of decoding a GPScarrier signal without performing the initial step of tracking the GPSsignal comprises: (A) receiving a phase modulated GPS signal by using aGPS antenna; (B) extracting a GPS data from the received phase modulatedGPS signal; and (C) computing a total probability of a current GPS databit being “one” or “zero” at a GPS time epoch by using a decodingalgorithm.

In one embodiment, the method of the present invention of decoding a GPScarrier signal without performing the initial step of tracking the GPSsignal further comprises: (D) using the Hamming code to correct residualdata bit errors, wherein the data bit correction capability of theHamming code is higher than the expected percentage of the residual databit errors.

In one embodiment, the method of the present invention of decoding a GPScarrier signal without performing the initial step of tracking the GPSsignal further comprises: (E) outputting corrected by the Hamming codeGPS data bit having the total probability obtained in the step (C4) ofbeing the actual received GPS data bit at the time epoch k for furtherprocessing.

In one embodiment of the present invention, the step (C) furthercomprises: (C1) obtaining an absolute data polarity via preamblesequence detection; C2) reading correlator I_(P) (inphase punctual) andcorrelator Q_(P) (quadrature punctual) at each epoch times; wherein anew GPS data bit is transmitted at each epoch time; (C3) computing thepartial probability of the decoded data bit r_(k) at time epoch k bycomputing the phase change between data bit phase d_(k) at time epoch kand data bit phase d_(k-1) at time epoch (k-1); (C4) computing a totalprobability of the decoded data bit r_(k) at time epoch k by summing thepartial probability obtained in step (C3) over the N preceding timeepochs (k-1), (k-2), . . . (k-N); and (C5) multiplying a new data bitr_(k) at time epoch k obtained in the step (C4) by the absolute datapolarity obtained in the step (C1) to obtain a data bit having the totalprobability obtained in the step (C4) of being an actual received GPSdata bit at the time epoch k.

BRIEF DESCRIPTION OF DRAWINGS

The aforementioned advantages of the present invention as well asadditional advantages thereof will be more clearly understoodhereinafter as a result of a detailed description of a preferredembodiment of the invention when taken in conjunction with the followingdrawings.

FIG. 1 depicts a block diagram of a GPS receiver of the presentinvention including novel Data Extraction capable of decoding GPS signalwith low SNR.

FIG. 2A shows in-phase (I) correlation outputs.

FIG. 2B illustrates quadrature (Q) correlation outputs.

FIG. 3 depicts a diagram of data modulation effect on GPS carriersignal.

FIG. 4 shows a diagram of phase locked loop lock position in IQ plane.

FIG. 5 illustrates a diagram of frequency locked loop phase position inIQ plane.

FIG. 6A depicts IQ plane data points corresponding to a signal having asignal-to-noise ratio (SNR) of 28 dB and at phase angle of 0°.

FIG. 6B shows IQ plane data points corresponding to a signal having SNRof 8 dB and at phase angle of 0°.

FIG. 7 depicts IQ plane data points corresponding to a signal having SNRof 8 dB and at phase angle of 45°.

FIG. 8A illustrates a phase angle computation for a signal having SNR of28 dB and at phase angle of 0°.

FIG. 8B shows a phase angle computation for signal having SNR of 8 dBand at phase angle of 0°.

FIG. 9 illustrates a sequence of data bit computations.

FIG. 10 is a flow chart of an implementation of the method of thepresent invention for decoding a GPS signal by using software running ona Microprocessor.

FIG. 11A shows a percentage of data bit errors for a signal having agiven SNR by using a linear y-axis scale.

FIG. 11B depicts a probability of a data bit error rate (BER) for asignal having a given SNR using a logarithmic y-axis scale.

FIG. 12A illustrates a prior art data bit stream decoded from a signalhaving SNR of 8 dB.

FIG. 12B is a data bit stream decoded from a signal having SNR of 8 dBby using the decoding method of the present invention.

FIG. 13 illustrates a diagram showing the effect of frequency offset ondata points in the IQ plane.

DETAILED DESCRIPTION OF THE PREFERRED AND ALTERNATIVE EMBODIMENTS

Reference will now be made in detail to the preferred embodiments of theinvention, examples of which are illustrated in the accompanyingdrawings. While the invention will be described in conjunction with thepreferred embodiments, it will be understood that they are not intendedto limit the invention to these embodiments. On the contrary, theinvention is intended to cover alternatives, modifications andequivalents that may be included within the spirit and scope of theinvention as defined by the appended claims. Furthermore, in thefollowing detailed description of the present invention, numerousspecific details are set forth in order to provide a thoroughunderstanding of the present invention. However, it will be obvious toone of ordinary skill in the art that the present invention may bepracticed without these specific details. In other instances, well knownmethods, procedures, components, and circuits have not been described indetail as not to unnecessarily obscure aspects of the present invention.

In one embodiment, the present invention relates to decoding of 50 Bauddata from GPS satellites under low signal-to-noise ratio (SNR)conditions. GPS satellites transmit signal power such that a receiver onthe surface of the Earth with clear view of the sky should expect toreceive signal power of at least −130 dBm. If ‘u’, is a real,nonnegative, power signal (units of watts), the dBm conversion isequivalent to performing the dB operation after converting the input tomilliwatts:y=10*log 10(u)+30   (Eq. 1)

For the transmit signal power details, please, see “GPS InterfaceControl Document”, ICD-GPS-200, IRN-200B-PR-OOJ, Rev. B-PR, U.S. AirForce, Jul. 1, 1992.

The received signal power may be translated into an SNR across each 50Baud data bit by taking into account noise sources, receiver losses andbandwidths. The received signal having −130 dBm power corresponds toapproximately to a signal having 28 dB SNR across each data bit. Atthese SNRs levels data the bit error rate (BER) is relatively low, thebit errors are very rare and can be easily detected and corrected via,for example, the data's forward error correction (FEC) capabilities. Inrecent years GPS operation has been extended to include indoor and otherapplications where the received signal power is expected to besubstantially reduced. For example, the received signal power target forindoor applications is −150 dBm that is 20 dB lower than the nominalsignal power. The received signal having −150 dBm power corresponds to asignal having an SNR across each data bit of 8 dB. At this SNR level (of8 dB) the data bit errors are much more frequent that data bit errors inthe case of a signal having 28 dB SNR across each data bit.

In addition, as another effect of low SNR conditions, the phase lockedloop (PLL) technique does not operate adequately for signals having SNRlevel of 8 dB or lower. Therefore, the phase locking the carriertracking loop in the GPS receiver becomes unreliable for signals havingSNR level of 8 dB or lower.

Unreliable phase locking can lead to false lock on signal sidebands andother loss of lock phenomena. Therefore, 50 Baud data decoding using thephase locking is very difficult. In the prior art, a common practiceused to ensure reliable signal tracking is to utilize a frequency lockedcarrier tracking loop under low SNR conditions. The prior art frequencylocked loop (FLL) provides reliable tracking but creates additionalproblems associated with 50 Baud data decoding. The present inventionallows one to overcome the prior art FLL data decoding problems and toachieve a reliable 50 Baud data decoding at SNRs lower than with priorart techniques, thus resulting in improved GPS receiver performance.

In one embodiment, FIG. 1 shows a high level block diagram 10 of thepresent invention. The satellite signals (not shown) are received via anAntenna block 12 and are further processed via an RF Section 14. In oneembodiment of the present invention, the RF Section 14 is configured todigitize the received satellite signal 13 thus providing an N-bitdigital signal 16 to a Digital Tracker block 18.

Referring still to FIG. 1, in one embodiment of the present invention,the Digital Tracker block 18 includes a plurality of digital mixers (notshown) and numerically controlled oscillators (NCOs) (not shown) forcarrier removal, and a C/A code generator (not shown) with logic forcorrelating with the incoming satellite code. The Digital Tracker 18facilitates tracking of code and carrier components of the incomingsatellite signal. The Antenna 12, RF Section 14 and Digital Tracker 18blocks have been previously described in detail in the U.S. Pat. No.5,621,416 “Optimized Processing of Signals for EnhancedCross-Correlation in a Satellite Positioning System Receiver”, issuedApr. 15, 1997. '416 patent is incorporated by reference herein in itsentirety.

More specifically, '416 patent discloses a satellite receiver configuredfor optimum correlation processing of L1 and L2 signals received from atleast one satellite. The satellite receiver of '416 patent includes adual frequency patch ANTENNA (not shown) for receiving the L1 and L2satellite signals; a FILTER/low noise amplifier (LNA) (not shown) forperforming filtering and low noise amplification of the L1 and L2signals; a DOWNCONVERTER (not shown) for mixing and converting the L1and L2 signals; and an IF PROCESSOR (not shown) for transforming theconverted L1 and L2 signals into digitally sampled quadrature versionsof L1 and L2 signals (IL1, QL1, IL2, QL2).

The satellite receiver of '416 patent includes the DIGITAL CHANNELPROCESSOR (not shown) including an L1 TRACKER (not shown) for trackingL1 C/A code when Y code is ON and for tracking L1 P code when Y code isOFF; an L2 TRACKER (not shown) for tracking an enhanced cross correlatedW code when Y code is ON and for tracking L2 P code when Y code is OFF;and a MICROPROCESSOR system (not shown). The L1 TRACKER is fed bydigitized inphase IL1 and quadrature QL1 of L1 signal outputted by theIF PROCESSOR. The L2 TRACKER is fed by digitized inphase IL2 andquadrature QL2 of L2 signal outputted by the IF PROCESSOR. TheMICROPROCESSOR system is fed by output signals from the L1 TRACKER andthe L2 TRACKER; and the L1 TRACKER and the L2 TRACKER are fed by controlsignal from the MICROPROCESSOR.

The L1 TRACKER of '416 patent provides a locally generated replica ofC/A code and P-code, multiplies digitized inphase IL1 and QL1 signalshaving carrier frequency with inphase and quadrature components ofdigital carrier, and performs code correlation with the locallygenerated replica of C/A code at 3 time points (early, punctual andlate) on the autocorrelation function graph creating an early, apunctual and a late sample of the autocorrelation function, andintegrates the IE (inphase early), the IP (inphase punctual), the IL(inphase late), the QE (quadrature early), the QP (quadrature punctual),and the QL (quadrature late) versions of the correlated samples of theL1 C/A (or P) code with the locally generated version of C/A (or P) codeacross a time period given by a multiple of L1 C/A EPOCH codes, whereinthe MICROPROCESSOR develops feedback signals for the carrier trackingloop and for the code tracking loop. The IE, IL, QE, and QL signals areused by the code tracking loop to form: (1) a code phaseestimate=K1(IE−IL), when the carrier loop is locked; or (2) a code phaseestimate=K1 [(IE²+QE²)^(1/2)−(IL²+QL²)^(1/2)], when the carrier loop isnot locked; K1 is an L1 code loop gain factor. The IP and QP signals areused by the carrier tracking loop by forming a carrier phaseestimate=arctan(QP/IP). Similarly, the L2 TRACKER of '416 patentperforms the same operations on the L2 signals as the L1 TRACKER on theL1 signals.

Referring still to FIG. 1, in one embodiment of the present invention,the Digital Tracker 18 provides correlation signals (I_(P) 22, Q_(P) 24and K_(corr) 26) to a Microprocessor block 20. The functions of theMicroprocessor 20 include closing code and carrier tracking loops viathe Control signal fed back to Digital Tracker block 18 (the briefexplanation was provided in the analysis of the '416 patent above).

In one embodiment of the present invention, the Digital Tracker 18includes a number of correlators used for different purposes includingsignal search, code tracking, carrier tracking and data decode (e.g.see'416 patent). The present invention focuses primarily on twocorrelators, the punctual in-phase correlation (I_(P)) and the punctualquadrature phase correlation (Q_(P)). Other correlators in the receiver,and there may be many, are represented by signal K_(corr). The primarypurpose of the I_(P) and Q_(P) correlators is to facilitate closing ofthe carrier tracking loop and to facilitate decoding of the 50 Bauddata.

FIGS. 2A and 2B show the signal amplitude of the various correlators.The x-axis represents the time delay between locally generated andincoming satellite generated C/A codes. Both I_(P) correlator 40 (ofFIG. 2A) and Q_(P) correlator 50 (of FIG. 2B) are formed at the maximumsignal time delay (when satellite and locally generated C/A codes arealigned). I_(P) and Q_(P) are chosen for data decode operation becausethey are points of maximum signal amplitude which in turn minimizes theprobability of data bit errors for a given SNR. The I_(P) and Q_(P)correlators are generated by mixing the incoming signal with carriersthat are 90° apart, in this way the receiver can measure the differencebetween the locally generated carrier signal and the incoming satellitecarrier signal by forming the function:C _(phase)=tan⁻¹(Q _(P) /I _(P));   (Eq. 2)where C_(phase) is a carrier phase offset between a locally generatedcarrier (in Digital Tracker 18 of FIG. 1) and an incoming satellitegenerated carrier.

According to Eq. 2, a change in the carrier phase C_(phase) causes achange in the relative amplitudes I_(P) 40 (of FIG. 2A) and Q_(P) 50 (ofFIG. 2B) of the signal, wherein the full amplitude of the signal givenby (I²+Q²)^(1/2) remains constant.

In one embodiment, the GPS data decoding method of the present inventionis associated with the carrier tracking because the GPS 50 Baud datastream modulation format involves phase modulating the GPS carrier. TheGPS data is modulated by using Binary Phase Shift Keying (BPSK). A newGPS data bit is transmitted every 20 milliseconds.

In one embodiment of the present invention, FIG. 3 illustrates the GPScarrier phase when modulated by data. The GPS data bit has two possibleoutcomes for the carrier, either the new data bit will leave the carrierphase unchanged or it will flip the carrier phase by 180°. Three databit periods of 20 milliseconds each are shown, (d₁ 62, d₂ 64, and d₃66). Transition from one data bit state to another occurs on 20millisecond boundaries t₁ 68 and t₂ 70. At data bit boundary t₁ 68 thephase of the carrier is continuous. This indicates that the new data bit(d₂ 64) is the same as the one transmitted before it (d₁ 62).

On the other hand, the new data bit (d₃ 66) starting transmission attime t₂ 70 causes an 180° phase shift in the carrier, indicating thatthe data bit d₃ 66 is of opposite polarity to the polarity of data bitd₂ 64. Thus, to determine the sequence of information bearing data bits,a receiver has to monitor the carrier phase.

In one embodiment of the present invention, FIG. 4 shows the basicrelationship 80 between I_(P) and Q_(P) correlation signals in thepresence of data bit transitions. FIG. 4 is known as an IQ plane plotand it illustrates the current carrier phase, C_(phase) as measured bythe GPS receiver. A PLL type carrier tracking loop typically seeks tominimize the signal amplitude in the Q_(P) correlation, thus minimizingC_(phase) according to (Eq. 2). FIG. 4 illustrates the ideal result ofsuch a PLL operation, with Q_(P) signal amplitude equal to zero. Theremaining signal amplitude equal to I_(P) [(I_(p) ²+Q_(p) ²)^(1/2) (atQ_(P)=0)=ÅI_(P)] is shown as two points on FIG. 4 with d_(k) 82 andd_(k-1) 84 representing the two possible signal points caused bydifferent data bit effects on the signal's carrier phase. A new data bitcauses an 180° phase shift (from (+)I_(P) to (−)I_(P), or from (−)I_(P)to (+)I_(P)) (as shown in FIG. 4), or zero phase shift (i.e. carrierphase remains at last point) (not shown).

In one embodiment of the present invention, FIG. 4 shows the data bittransition from d_(k-1) 84 to d_(k) 82 of 180°, thus indicating thatdata bit d_(k) 82 is opposite in polarity from data bit d_(k-1) 84. GPSreceivers typically decode the data (for instance, the data presented inFIG. 4) by observing the sign of the current I_(P) signal. Under theseconditions each data bit is decoded independently of other data bitsaround it. Absolute polarity of the data bits further involves decodingthe Preamble sequence included in the GPS data message. (Please, see“Global Positioning System: Theory and Applications”, Volume 1, pages121-176, third printing, 1996, for details). For the purpose of thepresent invention, a positive I_(P) of FIG. 4 is decoded as a binary‘1’, and a negative I_(P) is decoded as a binary ‘0’. It is known to aperson skillful in the art, to also refer to the binary data bitpossibilities as ‘−1’ and ‘+1’.

In one embodiment of the present invention, FIG. 5 shows a possible IQplane plot 90 when phase locking the carrier is no longer possible andinstead of using the phase lock loop (PLL) one has to use a frequencylock loop (FLL) to track and lock on a carrier signal. Under FLLtracking the phase of the signal in the IQ plane can take on any valueand is not restricted to signal energy lying on the I_(P) axis.Therefore, the sign of only I_(P) correlation is no longer adequate toperform data bit decoding, because the contribution of Q_(P) correlationcannot be ignored. With FLL tracking the typical data decoding algorithmdifferentiates a binary ‘0’ and ‘1’ by determining if a phase transitionof 0° or 180° has occurred between data bits. However, the FLLtracking-based data decoding has ‘memory’ (as opposed to PLLtracking-based data decoding that has no memory) in that the probabilityof current data bit being decoded correctly is dependent on the accuracyof the previous data bits decoding. Therefore, if the previous data bitis decoded wrongly the probability of the current data bit being wronglydecoded is relatively high and cannot be ignored. This dependence on theaccuracy of previous data bits is at the core of the major problem withdecoding data while using an FLL tracking method. The present inventionspecifically deals with this problem, as it is fully described below.

FIG. 6A shows the IQ plane plot 100 when noise is added such that theSNR observed is approximately 28 dB. It is observed that two clearlydefined small groups of data points: a group 102 of data points havingdata bit polarity (−1) and a group 104 of data points having data bitpolarity (+1) are formed. FIG. 6A illustrates that when SNR is high itis relatively easy to distinguish one data bit polarity from another.The thick dashed line 106 of FIG. 6A represents the data bit decisionthreshold.

On the other hand, FIG. 6B shows the equivalent IQ plane plot 110 whenthe SNR is 8 dB. It is observed from FIG. 6B that it is more difficultto distinguish a group 112 of data bits approximately having data bitpolarity (−1) and a group 114 of data points approximately having databit polarity (+1) from each other. Indeed, the high noise, or low SNR,causes the data points go beyond the decision threshold line 116 so thatthe data bit errors occur. If data points go beyond the threshold line116 far enough, the groups 112 and 114 of data points intersect, so thatthe data point (+1) can be interpreted as the data point (−1), and viceversa.

FIG. 7 shows the combined effect of FLL and low SNR (8 dB) on the IQplane plot 120. The FLL tracking means that the absolute carrier phaseis not known and the GPS receiver attempts to detect the change incarrier phase to facilitate data decoding. The prior art algorithms thatwere typically used to decode data under these conditions are describedbelow.

Indeed, the carrier phase transition between data bits can be computedusing a number of different algorithms. Equations 3 and 4 (please, seebelow) represent two such algorithms. Each algorithm (according toEquation 3, or according to Equation 4) fundamentally performs the sametask that is computing the probability of whether the data bittransition is closer to 0° or 180°.

In the first prior art algorithm of computing the probability of whetherthe data bit transition is closer to 0° or 180°, C_(phase k) is thecarrier phase at time k, and C_(phase k) is computed by using functionatan⁻¹(Q_(Pk)/I_(Pk)):P _(trans) =abs(C _(phase k) −C _(phase k-1)).   (Eq. 3)Here, Abs ( ) takes the absolute value.

In the second prior art algorithm of computing the probability ofwhether the data bit transition is closer to 0° or 180°, the calculationof cos(C_(phase)) is simplified while computing the scalar product:P _(trans)=(I _(Pk) I _(Pk-1) +Q _(Pk) Q _(Pk-1))<0   (Eq. 4)

FIGS. 8A and 8B show the result of measuring the carrier phase changebetween data bits for SNR of 28 dB (plot 130 of FIG. 8A) and for SNR of8 dB (plot 140 of FIG. 8B) respectively. The thick dashed line (136 ofFIG. 8A and 142 of FIG. 8B) again represents the data bit decisionthreshold. Once again it is observed that lower SNR causes more datapoints to approach (or cross, thus causing the data bit error) thedecision threshold. FIGS. 8A and 8B are produced by using (Eq. 4).

As was stated above, the data decoding while using FLL tracking isdependent on whether the previous data bits were decoded correctly(memory effect). This memory effect manifests itself in a prior data biterror (or incorrectly decoded data bit) causing all subsequent data bitsto be decoded incorrectly. FIG. 12A shows the effect of such errors(string of data bits 190) on a GPS data frame of 1500 data bits. The‘0’s and ‘1’s represent correctly decoded data bits. The ‘x’s indicatewrongly decoded data bits (data bit errors). It is observed that databit errors occur in long strings, this is the effect of a single databit error causing all subsequent data bits to be wrong (or at leastuntil another data bit error corrects the data decoding). The GPS 50Baud data stream has an extended Hamming code for error detection andcorrection (please, see “Global Positioning System: Theory andApplications”, Volume 1, pages 121-176, third printing, 1996, fordetails). The Hamming code can correct 1 data bit error for every 30data bits sent (or roughly 3.3% of errors), and can detect 3 data biterrors for every 30 data bits sent. The data bit errors shown in FIG.12A would overwhelm the data error correcting capacity of the Hammingcode and render the data decode useless. Note that FIG. 12A shows theresult of using one of the prior art data decoding algorithms at SNR 8dB, but without having the benefit of implementing the decoding method(or decoding algorithm) of the present invention.

On the other hand, FIG. 12B illustrates (string of bits 200) the samedecoding conditions as shown in FIG. 12A, but implementing the decodingmethod (or decoding algorithm) of the present invention. (Please, seefull discussion below). From FIG. 12B it is observed that when thepresent invention is implemented, a single data bit error does not causeall subsequent bits to be in error, thus substantially reducing thenumber of data errors. Therefore, the subsequent usage of Hamming code'scapabilities can further reduce (or correct) the data bit errors.

FIGS. 11A and 11B show the impact of SNR on data bit errors assumingthat data bit errors do not cause all subsequent data bits to be inerror. FIG. 11A illustrates (please, see curve 170) that with an SNR of8 dB the expected percentage of data bit errors is around 2% if thedecoding method of the present invention is implemented. This is lowerthan the 3.3% data bit correction capability of the Hamming code,indicating that most data bit errors could be corrected and most 30 bitGPS data words are correctly decoded.

FIG. 11B is a logarithmic plot 180 of the curve 170 of FIG. 11A. Plot180 of FIG. 11B illustrates that even at higher SNRs (e.g. 11 dB), databit errors still occur with enough frequency to cause data decodeproblems. For example, at SNR=11 dB, there is a significant probability(10⁻³) of data error, that is at least one data bit error is to beexpected in a GPS data frame of 1500 bits. However, as opposed to theprior art decoding algorithms, a single data bit error does not causeall subsequent data bits to be in error. If a prior art decodingalgorithm is used, a data bit error probability would be much higherthan 10⁻³, closer to 0.5, overwhelming the Hamming code's correctioncapabilities.

In the prior art the data bit phase transition was computed betweencurrent and last data bits, then multiplied by the data polarity of thelast data bit, as shown in Equation 5.r _(k) =sgn(P _(trans k-1) ×r _(k-1)).   (Eq. 5)

However, Eq. 5 does not reflect the fact that the result is alsomultiplied by the absolute data polarity determined from the Preamblesequence.

The algorithm used in the decoding method of the present inventioncomputes the current data bit by computing the phase transition betweenthe current bit and the last N data bits. In this way the calculation ofthe probability of the current bit being “1” or “0” is less dependent onthe last data bit phase calculation, but is based, instead, on amajority decision average of the last N phase transitions. This reducesthe contribution of the partial probability that the last data bitdecision (r_(k-1)) is wrongly computed in the total probability of thecurrent data bit being correctly computed. Therefore, the ‘memory’effect is significantly reduced. In fact, the performance of thedecoding algorithm of the present invention in the FLL tracking caseapproaches (but does not exceed) that of the PLL tracking case.

The decoding algorithm used in the decoding method of the presentinvention performs the calculation of probability according to Equation6:r _(k) =sgn(Σ_(1 . . . N)(P _(trans k-n) ×r _(k-n)));   (Eq. 6)where, r_(k) is the resulting data decode at time k, sgn is the sign ofoperation resulting in +/−1 output, P_(trans k-n) is the phasetransition calculation shown in Equations 3 and 4 at time k-n, r_(k-1)is the data decode output at time k-N.

The calculation of Equation 6 sums across N P_(trans k-n)×r_(k-n)calculations. FIG. 9 shows the current phase d_(k) 142 and previous Ndata bit phases d_(k-N) 150, . . . d_(k-3) 148, d_(k-2) 146, and d_(k-1)144. To compute the new data bit r_(k), one has to compute the phasechange between data time d_(k) and d_(k-1) and multiply by the datadecision already made at time k-1, r_(k-1). This result is summed withthe same operation performed between data time d_(k) and d_(k-2) andmultiplied by the data decision already made at time k-2, r_(k-2). Thisoperation is continued between d_(k) and d_(k-n), resulting in asummation that is positive if a majority of the individual phasetransitions suggest that the data bit is positive, and negativeotherwise. Once again absolute data polarity is obtained by multiplyingthe r_(k) value by the data polarity determined via the GPS dataPreamble, not shown in Equation 6.

The larger N, the more of the previous data bit phases are used in thecalculation, which further reduces the probability of a sequence of databit errors. However, in practice it is not feasible to use a large N(e.g. N>20) because of the phase drift caused by small frequency errors,as illustrated in diagram 210 of FIG. 13. If the phase shiftssignificantly (e.g. >45°) across the N+1 data bits used by the decodingalgorithm of the present invention, Equation 6 produces an incorrectresult. Thus choice of an optimum N depends on frequency drift errors inthe particular GPS receiver implementation. Some receivers have moreaccurate oscillators and less user motion where larger N could beutilized to further reduce the probability of data bit errors.

In one embodiment, FIG. 10 shows a flow diagram 150 of the softwarealgorithm used to implement the present invention. The first operation(at step 152) is to determine absolute data bit polarity via Preamblesequence detection. Correlators I_(P) and Q_(P) are then read at 20millisecond intervals (step 154). Then the phase transition is computed(at step 156) between the current and last data bits. The calculation ofEquation 6 is then performed (at step 158) across the previous N databits and the current data bit. The resulting data bit r_(k) is thenoutput (at step 160) and multiplied by the absolute data polarity (atstep 162). At the next step a data correction code is used to correctany data bit errors. In one embodiment of the present invention, (step164) the Hamming code is used to correct any data bit errors. If theHamming code is used, it is performed across a 30 bit data word, so itis performed every 30 bits. At the next step (step 166) the data bitsare output for use in other applications, including for internalreceiver's use for navigation.

There are several applications in the field of GPS receiver systems thatcan benefit directly from the ability to get a better bit error rate indecoding the Satellite Data Message from the GPS satellites. Theseapplications include survey receivers, geographic information systems(GIS) receivers, chipsets for use in cellphones, in-vehicle tracking andnavigation systems, package tracking systems, and military applicationsusing both coarse acquisition service and the precise service (P code orY code.) All of these applications experience obscured signal paths fromthe satellites, resulting in reduced SNR.

The given above disclosure assumes the usage of GPS received of anaverage quality. However, if a very good GPS receiver oscillator is usedand the GPS receiver is not moving, it is possible to predict thecarrier frequency without using the FLL tracking. In this embodiment ofthe present invention, the method of decoding a GPS carrier signalwithout performing the initial step of tracking the GPS signal comprisesthe following steps: (A) receiving a phase modulated GPS signal by usinga GPS antenna; (B) extracting a GPS data from the received phasemodulated GPS signal; and (C) computing a total probability of a currentGPS data bit being “one” or “zero” at a GPS time epoch by computing aplurality of probabilities of phase transitions at a plurality of GPStime epochs, wherein each probability of a phase transition at the GPStime epoch is a probability of a phase transition between a currentphase of the received GPS phase modulated signal and a phasecorresponding to a previously computed data bit. In one embodiment, thestep (C) is performed by using the algorithm according to Equation 6.

The present invention described above is fully applicable to anysatellite based signal, not necessarily to the GPS-emanated signals. Forinstance, the present invention is applicable to GLONASS-emanatedsignals, GALILEO-emanated signals, or combined GPS-GLONASS-GALILEOemanated signals.

The present invention is also fully applicable to decoding of signalsgenerated by any ground based transmitter and having the propertiessimilar to a GPS signal.

Another aspect of the present invention is directed to a method ofdecoding a received phase modulated carrier signal of an arbitrarynature, not necessarily a GPS based signal, satellite-based signal, oreven ground-transmitter-based signal. In one embodiment of the presentinvention, the method of decoding a received phase modulated carriersignal comprises the following steps: (A) computing a total probabilityof a current data bit being “one” or “zero” at a time epoch by computinga plurality of probabilities of phase transitions at a plurality of timeepochs, each probability of a phase transition at one time epoch being aprobability of a phase transition between a current phase of thereceived phase modulated signal and a phase corresponding to apreviously computed data bit; and (B) outputting the current data bit asbeing “one” or “zero” at the time epoch based on the computed in thestep (A) total probability. In this embodiment, the assumption has beenmade that the signal (of arbitrary nature) that has to be decoded hasbeen already successfully received. In one embodiment of the presentinvention, the step (A) is performed by using the Equation 6 (as wasdiscussed fully above). Thus, though the present invention has beendescribed above in terms of GPS data decoding, it is equally applicableto the decoding of any phase modulated signals in other systems. In itsbroadest terms, the invention involves using multiple previous data bitstransition information to reduce the probability of causing an extendedsequence of data bit errors, as was present in the prior art techniques.The invention reduces the SNR required for successful data decoding.

The foregoing description of specific embodiments of the presentinvention have been presented for purposes of illustration anddescription. They are not intended to be exhaustive or to limit theinvention to the precise forms disclosed, and obviously manymodifications and variations are possible in light of the aboveteaching. The embodiments were chosen and described in order to bestexplain the principles of the invention and its practical application,to thereby enable others skilled in the art to best utilize theinvention and various embodiments with various modifications as aresuited to the particular use contemplated. It is intended that the scopeof the invention be defined by the claims appended hereto and theirequivalents.

1. A method of decoding a GPS carrier signal without performing theinitial step of tracking, said method comprising: (A) receiving a phasemodulated GPS signal by using a GPS antenna; (B) extracting a GPS datafrom said received phase modulated GPS signal; (C1) obtaining anabsolute data polarity via preamble sequence detection; (C2) readingcorrelator I_(P) (inphase punctual) and correlator Q_(P) (quadraturepunctual) at each epoch times; wherein a new GPS data bit is transmittedat each said epoch time; (C3) computing the partial probability of thedecoded data bit r_(k) at time epoch k by computing the phase changebetween data bit phase d_(k) at time epoch k and data bit phase d_(k-1)at time epoch (k-1); (C4) computing a total probability of the decodeddata bit r_(k) at time epoch k by summing the partial probabilityobtained in step (C3) over the N preceding time epochs (k-1), (k-2), . .. (k-N); and (C5) multiplying a new data bit r_(k) at time epoch kobtained in said step (C4) by said absolute data polarity obtained insaid step (C1) to obtain a data bit having said total probabilityobtained in said step (C4) of being an actual received GPS data bit atsaid time epoch k.
 2. The method of claim 1, wherein said step (C3)further comprises: (C3, 1) computing the partial probability of thedecoded data bit r_(k) at time epoch k by computing the scalar productof vector (I_(Pk), Q_(Pk)) at time epoch ‘k’ and vector (I_(Pk-1),Q_(Pk-1)) at time epoch ‘k-1’.